Separating different buckets of your life is hard. It is hard not let your emotions reflect your reality. When someone offends you and you do not deal with the emotion, your often will in-turn hurt someone else, not on purpose, but because that emotion needs to go somewhere. Embracing emotions means you take the time to dissect them and break them down before you need to move on to your next task or relationship. An easy way to do this is to ask, is what I am feeling really going to be important to me 2 years from now? Will this feeling have any impact on my life then? If not, then you can put the emotion in its proper place and let it flow through you and be done, having run its course. When you do this, you can move on and approach every new person and situation with your best self.